What is 82.5% of 2,360?

Introduction / Context:
This question is a direct computation of a given percentage of a number. Calculating 82.5% of 2360 helps reinforce how to handle percentages that are not whole numbers, especially those involving halves such as 0.5%. This skill is useful in many real life contexts, including discounts, scores, and financial calculations.

Given Data / Assumptions:

• We need to find 82.5% of 2360.
• 82.5% is a fractional percentage consisting of 82% plus 0.5%.
• No additional conditions or adjustments are given.

Concept / Approach:
To find X% of a number N, we can either convert X% to a decimal and multiply or break X% into simpler parts. Here, 82.5% can be written as 82.5 / 100 = 0.825. So we can compute 0.825 * 2360. Alternatively, we can split 82.5% into 80% + 2% + 0.5% of 2360, compute each part separately, and sum them. This second approach provides an easy mental calculation method and improves understanding of how percentages break down.

Step-by-Step Solution:
Step 1: Write 82.5% as a decimal: 82.5% = 82.5 / 100 = 0.825. Step 2: Multiply 0.825 by 2360: 0.825 * 2360. Step 3: Break it into components: 0.825 * 2360 = (0.8 + 0.02 + 0.005) * 2360. Step 4: Compute 80% of 2360: 0.8 * 2360 = 1888. Step 5: Compute 2% of 2360: 0.02 * 2360 = 47.2. Step 6: Compute 0.5% of 2360: 0.005 * 2360 = 11.8. Step 7: Add the parts: 1888 + 47.2 + 11.8 = 1947. Step 8: Therefore, 82.5% of 2360 is 1947.

Verification / Alternative check:
We can verify by direct decimal multiplication: 0.825 * 2360. Using standard multiplication, 825 * 2360 / 1000 yields 1947. This confirms the result obtained via percentage decomposition. Both methods support that the correct value is 1947.

Why Other Options Are Wrong:
1960, 1954, and 1931 are close to 1947 but do not match the exact calculated value. They may correspond to incorrect approximations or rounding at intermediate steps. The option 2025 is significantly higher and clearly not correct. Only 1947 matches the precise computation of 82.5% of 2360.

Common Pitfalls:
Common mistakes include treating 82.5% as 0.8250 but then misaligning decimal places during multiplication, or mistakenly computing 82.5% as 0.8250 of 236 instead of 2360. Some learners also forget to include the 0.5% component or treat it as 5% by mistake. Ensuring careful decimal conversion and organized computation avoids these errors.

Final Answer:
The value of 82.5% of 2360 is 1,947.